How do Rosencrantz and Guildenstern behave around Hamlet?

In Act II, Scene 2 of Hamlet, we see that King Claudius has sent for Hamlet's two schoolmates Rosencrantz and Guildenstern in the hope that they can learn what is really on Hamlet's mind and report this information back to him. It was just a few months ago that the three young men were schoolmates at Wittenberg, and they still joke together, mainly about the opposite sex, the way young men will do. Although both Rosencrantz and Guildenstern have remained the same unworldly, party-loving students, Hamlet has changed very much as a result of all he has been through in this short time.
One of the ways that Rosencrantz and Guildenstern function in the play is to serve as contrasts, or foils, to the exceptionally clever Prince. They remain the same clueless young men throughout, while he evolves before our eyes into a serious, determined, mature and regal person. It is appropriate that Rosencrantz and Guildenstern immediately announce the arrival of the troop of traveling actors when they meet Hamlet because their obvious interest in entertainment helps to characterize them. They are simple souls who have been given the delicate task of analyzing the thoughts, feelings, and motives of their old friend, who is now miles ahead of them in maturation. They have to try to do this without letting him suspect that this is what they were sent for. Hamlet can see through them as if they are transparent. This was probably not the case just a short time ago when they were all lighthearted schoolmates together, with nothing to worry about but reading books and turning in papers.